The Topological Pressure of Linear Cellular Automata

doi:10.3390/e11020271

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Entropy 2009, 11(2), 271-284; doi:10.3390/e11020271

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The Topological Pressure of Linear Cellular Automata

Jung-Chao Ban ^{1, 2} and Chih-Hung Chang ³^,*

¹ Department of Applied Mathematics, National Dong Hwa University, 97063, Hualian, Taiwan, R.O.C. ² Taida Institute for Mathematical Sciences, National Taiwan University, 10617, Taipei, Taiwan, R.O.C. ³ National Center for Theoretical Sciences, Mathematics Division, National Tsing Hua University, 30043, Hsinchu, Taiwan, R.O.C.

* Author to whom correspondence should be addressed.

Received: 13 April 2009 / Accepted: 6 May 2009 / Published: 11 May 2009

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Abstract: This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant. The formulae of measure-theoretic and topological entropies can be expressed in closed forms and the topological pressure is demonstrated explicitly for potential functions that depend on finitely many coordinates. According to these results, Parry measure is inferred to be an equilibrium measure.

Keywords: Cellular automata; additive; equilibrium measure

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MDPI and ACS Style

Ban, J.-C.; Chang, C.-H. The Topological Pressure of Linear Cellular Automata. Entropy 2009, 11, 271-284.

AMA Style

Ban J.-C., Chang C.-H. The Topological Pressure of Linear Cellular Automata. Entropy. 2009; 11(2):271-284.

Chicago/Turabian Style

Ban, Jung-Chao; Chang, Chih-Hung. 2009. "The Topological Pressure of Linear Cellular Automata." Entropy 11, no. 2: 271-284.

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